Inventory storage facilities such as warehouses and distribution centers commonly employ shelving units to hold inventory items until they are needed to fulfill a customer order. The shelving units are arranged in rows that are spaced from one another so as to define aisles between the rows of shelving units. To store an inventory item on a desired shelving unit, a human can carry the inventory item down an aisle in the warehouse to the desired shelving unit and place the inventory item on the desired shelving unit where it is stored until it is needed. When an order is placed, a human can travel down the aisle to the desired shelving unit, retrieve the inventory item from the desired shelving unit, and place the inventory item on a conveyor belt that carries the inventory item downstream for packaging and shipping. There are some systems in which containers are oriented in rows, and the entire row moves up or down vertically under the control of an operator.